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Entropy Production in Exactly Solvable Systems

Department of Mathematics, Imperial College London, 180 Queen’s Gate, London SW7 2AZ, UK
Centre for Complexity Science, Imperial College London, London SW7 2AZ, UK
The Francis Crick Institute, 1 Midland Rd, London NW1 1AT, UK
DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
Department of Physics, Imperial College London, Exhibition Road, London SW7 2AZ, UK
Author to whom correspondence should be addressed.
These authors have contributed equally to this work.
Entropy 2020, 22(11), 1252;
Received: 8 October 2020 / Revised: 30 October 2020 / Accepted: 1 November 2020 / Published: 3 November 2020
(This article belongs to the Special Issue Nonequilibrium Thermodynamics and Stochastic Processes)
The rate of entropy production by a stochastic process quantifies how far it is from thermodynamic equilibrium. Equivalently, entropy production captures the degree to which global detailed balance and time-reversal symmetry are broken. Despite abundant references to entropy production in the literature and its many applications in the study of non-equilibrium stochastic particle systems, a comprehensive list of typical examples illustrating the fundamentals of entropy production is lacking. Here, we present a brief, self-contained review of entropy production and calculate it from first principles in a catalogue of exactly solvable setups, encompassing both discrete- and continuous-state Markov processes, as well as single- and multiple-particle systems. The examples covered in this work provide a stepping stone for further studies on entropy production of more complex systems, such as many-particle active matter, as well as a benchmark for the development of alternative mathematical formalisms. View Full-Text
Keywords: entropy production; active matter; exact results; stochastic thermodynamics entropy production; active matter; exact results; stochastic thermodynamics
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MDPI and ACS Style

Cocconi, L.; Garcia-Millan, R.; Zhen, Z.; Buturca, B.; Pruessner, G. Entropy Production in Exactly Solvable Systems. Entropy 2020, 22, 1252.

AMA Style

Cocconi L, Garcia-Millan R, Zhen Z, Buturca B, Pruessner G. Entropy Production in Exactly Solvable Systems. Entropy. 2020; 22(11):1252.

Chicago/Turabian Style

Cocconi, Luca, Rosalba Garcia-Millan, Zigan Zhen, Bianca Buturca, and Gunnar Pruessner. 2020. "Entropy Production in Exactly Solvable Systems" Entropy 22, no. 11: 1252.

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